tetraflexagon_diagram: add a function to calculate the tile offset in a square

[flexagon-toolkit.git] / src / diagram / diagram.py

diff --git a/src/diagram/diagram.py b/src/diagram/diagram.py
index eee9fc6..e6c51c4 100755 (executable)
--- a/src/diagram/diagram.py
+++ b/src/diagram/diagram.py
@@ -32,6 +32,87 @@ class Diagram(object):
         raise NotImplementedError
 
     @staticmethod
         raise NotImplementedError
 
     @staticmethod

+    def test(diagram):
+        diagram.clear()
+
+        x = 40
+        y = 200
+
+        x_offset = x
+
+        theta = 0
+
+        diagram.draw_line(0, y, 400, y, (1, 0, 0, 1))
+
+        advance = diagram.draw_centered_text(x_offset, y, "Ciao", theta,
+                                             align_baseline=True,
+                                             bb_stroke_color=(0, 0, 0, 0.5),
+                                             bb_fill_color=(1, 1, 1, 0.8))
+        x_offset += advance
+
+        advance = diagram.draw_centered_text(x_offset, y, "____", theta + pi / 4,
+                                             align_baseline=True,
+                                             bb_stroke_color=(0, 0, 0, 0.5),
+                                             bb_fill_color=(1, 1, 1, 0.8))
+        x_offset += advance
+
+        advance = diagram.draw_centered_text(x_offset, y, "jxpqdlf", theta + pi / 2,
+                                             align_baseline=True,
+                                             bb_stroke_color=(0, 0, 0, 0.5),
+                                             bb_fill_color=(1, 1, 1, 0.8))
+        x_offset += advance
+
+        advance = diagram.draw_centered_text(x_offset, y, "pppp", theta + 3 * pi / 4,
+                                             align_baseline=True,
+                                             bb_stroke_color=(0, 0, 0, 0.5),
+                                             bb_fill_color=(1, 1, 1, 0.8))
+        x_offset += advance
+
+        advance = diagram.draw_centered_text(x_offset, y, "dddd", theta + pi,
+                                             align_baseline=True,
+                                             bb_stroke_color=(0, 0, 0, 0.5),
+                                             bb_fill_color=(1, 1, 1, 0.8))
+        x_offset += advance
+
+        advance = diagram.draw_centered_text(x_offset, y, "Jjjj", theta + 5 * pi / 4,
+                                             align_baseline=True,
+                                             bb_stroke_color=(0, 0, 0, 0.5),
+                                             bb_fill_color=(1, 1, 1, 0.8))
+        x_offset += advance
+
+        advance = diagram.draw_centered_text(x_offset, y, "1369", theta + 3 * pi / 2,
+                                             color=(0, 1, 0),
+                                             align_baseline=True,
+                                             bb_stroke_color=(0, 0, 0, 0.5),
+                                             bb_fill_color=(1, 1, 1, 0.8))
+        x_offset += advance
+
+        advance = diagram.draw_centered_text(x_offset, y, "qqqq", theta + 7 * pi / 4,
+                                             align_baseline=True,
+                                             bb_stroke_color=(0, 0, 0, 0.5),
+                                             bb_fill_color=(1, 1, 1, 0.8))
+        x_offset += advance
+
+        diagram.draw_rect(40, 40, 300, 100, stroke_color=(0, 0, 0, 0.8))
+        diagram.draw_rect(40, 40, 300, 100, pi / 30, stroke_color=(0, 0, 0, 0.8))
+
+        verts = diagram.draw_regular_polygon(190, 90, 3, 20)
+
+        diagram.draw_rect(40, 250, 300, 100, stroke_color=(0, 0, 0, 0.8))
+        diagram.draw_rect_from_center(40 + 150, 250 + 50, 300, 100, theta=(pi / 40),
+                                      stroke_color=(1, 0, 0),
+                                      fill_color=None)
+
+        verts = diagram.draw_regular_polygon(190, 300, 6, 20, pi / 3., (0, 0, 1, 0.5), (0, 1, 0.5))
+        diagram.draw_apothem_star(190, 300, 6, 20, 0, (1, 0, 1))
+
+        diagram.draw_star_by_verts(190, 300, verts, (1, 0, 0, 0.5))
+        diagram.draw_star(190, 300, 6, 25, 0, (1, 0, 1, 0.2))
+
+        diagram.draw_circle(190, 300, 30, (0, 1, 0, 0.5), None)
+        diagram.draw_circle(100, 300, 30, (1, 0, 0, 0.5), (0, 1, 1, 0.5))
+
+    @staticmethod

     def color_to_rgba(color):
         assert len(color) >= 3
 
     def color_to_rgba(color):
         assert len(color) >= 3
 


@@ -46,6 +127,66 @@ class Diagram(object):
         return fmod(theta, 2 * pi) / (2 * pi)
 
     @staticmethod
         return fmod(theta, 2 * pi) / (2 * pi)
 
     @staticmethod

+    def calc_rotate_translate_transform(src_x, src_y, dest_x, dest_y, theta):
+        """Calculate the transformation matrix resulting from a rotation and
+        a translation.
+
+        Return the matrix as a list of values sorted in row-major order."""
+
+        # A rotate-translate transformation is composed by these steps:
+        #
+        #   1. rotate by 'theta' around (src_x, src_y);
+        #   2. move to (dest_x, dest_y).
+        #
+        # Step 1 can be expressed by these sub-steps:
+        #
+        #  1a. translate by (-src_x, -src_y)
+        #  1b. rotate by 'theta'
+        #  1c. translate by (src_x, src_y)
+        #
+        # Step 2. can be expressed by a translation like:
+        #
+        #  2a. translate by (dest_x - src_x, dest_y - src_y)
+        #
+        # The consecutive translations 1c and 2a can be easily combined, so
+        # the final steps are:
+        #
+        #  T1 -> translate by (-src_x, -src_y)
+        #  R  -> rotate by 'theta'
+        #  T2 -> translate by (dest_x, dest_y)
+        #
+        # Using affine transformations these are expressed as:
+        #
+        #      | 1  0  -src_x |
+        # T1 = | 0  1  -src_y |
+        #      | 0  0       1 |
+        #
+        #      | cos(theta)  -sin(theta)  0 |
+        # R  = | sin(theta)   cos(theta)  0 |
+        #      |          0            0  1 |
+        #
+        #      | 1  0  dest_x |
+        # T2 = | 0  1  dest_y |
+        #      | 0  0       1 |
+        #
+        # Composing these transformations into one is achieved by multiplying
+        # the matrices from right to left:
+        #
+        #   T = T2 * R * T1
+        #
+        # NOTE: To remember this think about composing functions: T2(R(T1())),
+        # the inner one is performed first.
+        #
+        # The resulting  T matrix is the one below.
+        matrix = [
+            cos(theta), -sin(theta), -src_x * cos(theta) + src_y * sin(theta) + dest_x,
+            sin(theta),  cos(theta), -src_x * sin(theta) - src_y * cos(theta) + dest_y,
+                     0,           0,                                                 1
+        ]
+
+        return matrix
+
+    @staticmethod

     def get_regular_polygon(x, y, sides, r, theta0=0.0):
         """Calc the coordinates of the regular polygon.
 
     def get_regular_polygon(x, y, sides, r, theta0=0.0):
         """Calc the coordinates of the regular polygon.
 


@@ -86,3 +227,22 @@ class Diagram(object):
         apothem_angle = theta + pi / sides
 
         return self.draw_star(cx, cy, sides, apothem, apothem_angle, stroke_color)
         apothem_angle = theta + pi / sides
 
         return self.draw_star(cx, cy, sides, apothem, apothem_angle, stroke_color)

+
+    def draw_rect(self, x, y, width, height, theta=0,
+                  stroke_color=None,
+                  fill_color=(1, 1, 1, 0.8)):
+        raise NotImplementedError
+
+    def draw_rect_from_center(self, cx, cy, width, height, theta=0.0,
+                              stroke_color=None,
+                              fill_color=(1, 1, 1, 0.8)):
+        # the position of the center of a rectangle at (0,0)
+        mx = width / 2.0
+        my = height / 2.0
+
+        # calculate the position of the bottom-left corner after rotating the
+        # rectangle around the center
+        rx = cx - (mx * cos(theta) - my * sin(theta))
+        ry = cy - (mx * sin(theta) + my * cos(theta))
+
+        self.draw_rect(rx, ry, width, height, theta, stroke_color, fill_color)